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Motion of a particle

  1. Feb 24, 2009 #1
    1. The problem statement, all variables and given/known data

    The two-dimensional motion of a particle is defined by the relationship [tex] r = \frac {1}{sin\theta - cos\theta} [/tex] and [tex] tan\theta = 1 + \frac {1}{t^2} [/tex], where [tex] r [/tex] and [tex] \theta [/tex] are expressed in meters and radians, respectively, and [tex] t [/tex] is expressed in seconds. Determine (a) the magnitudes of velocity and acceleration at any instant, (b) the radius of curvature of the path.


    2. Relevant equations

    [tex] r = \frac {1}{sin\theta - cos\theta} [/tex]


    [tex] tan\theta = 1 + \frac {1}{t^2} [/tex]



    3. The attempt at a solution

    I've made a few attempts but they seem way more complicated than the problem should be I think. I'm assuming I need to solve [tex] tan\theta [/tex] for [tex] \theta [/tex]. Once i've done that I figure I'd need to differentiate both [tex] r [/tex] and [tex] \theta [/tex] to find [tex] \dot{r}, \ddot{r}, \dot{\theta}, \ddot{\theta}[/tex].

    I don't know if I'm on the correct route but any help would be appreciated. thanks!
     
  2. jcsd
  3. Feb 25, 2009 #2

    gabbagabbahey

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    Tangent is not a one-to-one function, so that's a bad idea.

    Instead, draw a picture!:smile: I think you can find expressions for [itex]\sin\theta[/itex] and [itex]\cos\theta[/itex] in terms of [itex]t[/itex] without actually solving for [itex]\theta[/itex] first.....think 'right triangle':wink:
     
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